Welcome!

I am a Postdoctoral Research Fellow at the Center of Mathematics and Artificial Intelligence, George Mason University, USA. I am working in the research group of Prof. Harbir Antil. Currently, I am working on the optimization problems governed by non-linear partial differential equations.

Research Interest

  • Numerical Analysis.
  • Finite Element Methods.
  • PDE-Constrained Optimization.
  • Deep Learning.

Work Experience

  • Postdoctoral Research Fellow (August 2023--Till Date)
    George Mason University, USA.
  • Assistant Professor in Mathematics (November 2022--July 2023)
    Government of Gujarat, India.

Education

  • PhD in Mathematics (2017-2022)
    Indian Institute of Technology (IIT) Delhi, India.
    PhD Supervisor: Prof. Kamana Porwal.
    Thesis Title: Pointwise A Posteriori Error Analysis for Elliptic Variational Inequalitites.
  • MSc in Mathematics (2014-16)
    Indian Institute of Technology (IIT) Madras, India.
  • BSc (H) in Mathematics (2010-14)
    Dyal Singh College, University of Delhi, India.

Publications

  • Khandelwal, R. and Porwal K. (2022):
    Pointwise a posteriori error analysis of a finite element method for the Signorini problem, Journal of Scientific Computing, 91(2):1--34 pp. DOI:10.1007/s10915-022-01811-0.
  • Khandelwal, R. and Porwal K. (2022):
    Pointwise a posteriori error analysis of quadratic finite element method for the elliptic obstacle problem, Journal of Computational and Applied Mathematics, 412, 114364. DOI: 10.1016/j.cam.2022.114364.
  • Khandelwal, R. and Porwal K. (2023):
    Pointwise a posteriori error control of discontinuous Galerkin methods for unilateral contact problems, Computational Methods in Applied Mathematics, 23(1):189--217 pp. DOI:10.1515/cmam-2021-0194.
  • Khandelwal, R. Porwal K. and Singla, R. (2023):
    Supremum-norm a posteriori error control of quadratic discontinuous Galerkin methods for the obstacle problem, Computers and Mathematics with Applications, 137:147--171 pp. DOI:10.1016/j.camwa.2023.02.003.
  • Khandelwal, R. Porwal K. and Wadhawan, T. (2023):
    Adaptive quadratic finite element method for unilateral contact problem, Accepted for publication in Journal of Scientific Computing. DOI:10.1007/s10915-023-02206-5.

Achievements

  • Secured 1st Rank in Assistant Professor (Mathematics) Examination conducted by Gujarat Public Service Commission 2019.
  • Passed GATE Examination 2017 with AIR (All India Rank) 34.
  • Passed National examination CSIR-UGC NET for PhD and Lectureship with AIR 60.
  • NBHM MA-MSc Scholarship 2015-16.
  • MERIT-CUM Scholarship, IIT Madras.
  • Secured AIR 140 in IIT JAM examination for Post Graduation study in IIT’s.
  • RAM LOBHIA MEMORIAL PRIZE, BSc (H) Mathrmatics (II year).

Invited Talks

  • 20 Oct--21 Oct, 2023: Finite Element Circus (Fall 2023) at University of Notre Dam, USA
Contact

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